Goal 2 Univaraite: US
Jaclyn A Coate
7/21/2020
US COVID Data
Data Prep
us <- read.csv("https://raw.githubusercontent.com/JaclynCoate/6373_Time_Series/master/TermProject/Data/USdaily7.19.csv", header = T, strip.white = T)
us <- transform(us, date = as.Date(as.character(date), "%Y%m%d"))
us <- subset(us, select = -c(states, dateChecked, hospitalized, lastModified, total, posNeg, totalTestResultsIncrease, hash))
us[is.na(us)] <- 0
#Selecting only those dates with reported current hospitilizations
us <- dplyr::slice(us,1:124)
us = us[order(as.Date(us$date, format = "%Y%m%d")),]
head(us)## date positive negative pending hospitalizedCurrently
## 124 2020-03-17 11928 63104 1687 325
## 123 2020-03-18 15099 84997 2526 416
## 122 2020-03-19 19770 108407 3016 617
## 121 2020-03-20 26025 138814 3330 1042
## 120 2020-03-21 32910 177262 3468 1436
## 119 2020-03-22 42169 213476 2842 2155
## hospitalizedCumulative inIcuCurrently inIcuCumulative
## 124 55 0 0
## 123 67 0 0
## 122 85 0 0
## 121 108 0 0
## 120 2020 0 0
## 119 3023 0 0
## onVentilatorCurrently onVentilatorCumulative recovered death
## 124 0 0 0 122
## 123 0 0 0 153
## 122 0 0 0 199
## 121 0 0 0 267
## 120 0 0 0 328
## 119 0 0 0 471
## totalTestResults deathIncrease hospitalizedIncrease negativeIncrease
## 124 75032 22 13 13707
## 123 100096 31 12 21893
## 122 128177 46 18 23410
## 121 164839 68 23 30407
## 120 210172 61 1912 38448
## 119 255645 143 1003 36214
## positiveIncrease
## 124 3613
## 123 3171
## 122 4671
## 121 6255
## 120 6885
## 119 9259Forecast Current Hospitalizations
It is difficult to assume stationarity for this data due to multiple factors. We are working under the assumption that COVID is a novel virus and cases as well as hospitalizations will eventually return to zero. This being said our current modeling techniques do things such as return to the median or mimic the previously seen trends. Also, we see a severe upward trend in both new cases and hospitalization would be dependent on this as well as time. We will review the data and see what, if any, non-stationary components reveal themselves and model the data accordingly.
Original Data Realization
Traits: - Heavy wandering behavior - What appears to be some noise that could be pseudo-cyclic behavior hidden by the large numbers.
ggplot(data = us, aes(x=date, y=hospitalizedCurrently))+
geom_line(color="orange")+
labs(title = "Current COVID Hospitalized Cases US", y = "Thousands", x = "") +
theme_hc()
Sample Realization, ACF, and Spectral Density
Realization - Heavy wandering behavior - Possible small pseudo-cyclic behavior ACF - Very slowly dampening behavior that would be consistent with a d=1 ARIMA model. Spectral Density - Peak at f=0 - What apepars to be a wave through the rest of the graph- this could be a hidden seasonailty cause another freq peak that is hidden by the pseudo-cyclic behavior mentioned in about the realization above.
plotts.sample.wge(us$hospitalizedCurrently)
## $autplt
## [1] 1.00000000 0.96469043 0.92302755 0.87525870 0.82267467
## [6] 0.76543844 0.70485512 0.64064756 0.57236121 0.50115588
## [11] 0.43487093 0.36990327 0.30454204 0.23997040 0.17553357
## [16] 0.11101329 0.04809253 -0.01338519 -0.07128970 -0.12337015
## [21] -0.17223727 -0.21557163 -0.25020503 -0.28191209 -0.30582707
## [26] -0.32569569
##
## $freq
## [1] 0.008064516 0.016129032 0.024193548 0.032258065 0.040322581
## [6] 0.048387097 0.056451613 0.064516129 0.072580645 0.080645161
## [11] 0.088709677 0.096774194 0.104838710 0.112903226 0.120967742
## [16] 0.129032258 0.137096774 0.145161290 0.153225806 0.161290323
## [21] 0.169354839 0.177419355 0.185483871 0.193548387 0.201612903
## [26] 0.209677419 0.217741935 0.225806452 0.233870968 0.241935484
## [31] 0.250000000 0.258064516 0.266129032 0.274193548 0.282258065
## [36] 0.290322581 0.298387097 0.306451613 0.314516129 0.322580645
## [41] 0.330645161 0.338709677 0.346774194 0.354838710 0.362903226
## [46] 0.370967742 0.379032258 0.387096774 0.395161290 0.403225806
## [51] 0.411290323 0.419354839 0.427419355 0.435483871 0.443548387
## [56] 0.451612903 0.459677419 0.467741935 0.475806452 0.483870968
## [61] 0.491935484 0.500000000
##
## $db
## [1] 11.5968519 12.3083066 11.5133997 7.4838113 3.3602139
## [6] 0.0335519 0.7084332 0.9156140 -0.8436600 -3.1819014
## [11] -5.4756678 -6.7623087 -6.8158311 -8.0631517 -7.3612462
## [16] -6.6859328 -6.5334837 -9.2703624 -6.9861347 -7.7480548
## [21] -9.2215880 -9.7427900 -9.8554763 -10.3609260 -12.4875682
## [26] -12.3111041 -12.5834700 -13.5552916 -13.3151569 -12.1559256
## [31] -13.3408790 -11.5752029 -11.5102517 -11.0062561 -13.6956455
## [36] -13.3799405 -12.8275350 -13.5948157 -13.7881199 -16.3540755
## [41] -16.1420426 -16.4026230 -16.3405545 -15.3322041 -13.6672886
## [46] -13.4609040 -13.7211937 -14.9264666 -15.4980009 -14.6885900
## [51] -14.1315883 -14.5816335 -17.2784109 -19.1817384 -15.4061574
## [56] -15.5625062 -15.6189618 -16.0617864 -14.7026778 -16.0503809
## [61] -14.3978563 -13.5639246
##
## $dbz
## [1] 10.712613 10.294626 9.591662 8.595197 7.295893 5.688294
## [7] 3.781244 1.619531 -0.679155 -2.892367 -4.749697 -6.121638
## [13] -7.103744 -7.844927 -8.408137 -8.813629 -9.124106 -9.444708
## [19] -9.862010 -10.401184 -11.025434 -11.666349 -12.267299 -12.809609
## [25] -13.299011 -13.732191 -14.084633 -14.333134 -14.485102 -14.579070
## [31] -14.658515 -14.750375 -14.865221 -15.010053 -15.196621 -15.437186
## [37] -15.732991 -16.066124 -16.401571 -16.698827 -16.925920 -17.067717
## [43] -17.126873 -17.121767 -17.083330 -17.048284 -17.048564 -17.101597
## [49] -17.206612 -17.348459 -17.506148 -17.660495 -17.796193 -17.899104
## [55] -17.954838 -17.953353 -17.896777 -17.802335 -17.696364 -17.604163
## [61] -17.543146 -17.522003Overfit tables
Since we are seeing heavy wandering behavior we will use overfit tables to see if we can surface any (1-B) factors that have roots very near the unit circle. - Below we are able to clearly see 1: (1-B) factor that has a root nearly on the Unit Circle.
est.ar.wge(us$hospitalizedCurrently,p=6,type='burg')##
## Coefficients of Original polynomial:
## 1.1909 0.0509 -0.0756 -0.0840 0.0023 -0.1042
##
## Factor Roots Abs Recip System Freq
## 1-1.9296B+0.9375B^2 1.0292+-0.0868i 0.9682 0.0134
## 1+0.9752B+0.3505B^2 -1.3911+-0.9580i 0.5921 0.4040
## 1-0.2365B+0.3172B^2 0.3729+-1.7361i 0.5632 0.2163
##
## ## $phi
## [1] 1.190923840 0.050864061 -0.075600901 -0.084022737 0.002285954
## [6] -0.104222855
##
## $res
## [1] -325.264880 50.930580 -96.193198 -125.387346 -374.281156
## [6] -194.078000 -456.418062 -92.886262 -133.725814 1281.535010
## [11] 1371.801436 -893.713641 -705.104613 -423.101902 189.943073
## [16] 490.314897 -112.058738 506.500493 2265.993568 -855.382812
## [21] 1291.660117 4913.615274 -1950.654296 2101.167402 -1561.969001
## [26] -236.630649 -2857.037527 -805.804218 2327.656472 -623.151634
## [31] -1344.365664 -880.889785 -966.611290 -767.681119 1256.494251
## [36] 3947.870486 -470.254103 -221.269559 -1555.374553 723.483060
## [41] -647.293020 934.135533 804.751750 742.703690 -592.440957
## [46] -808.895314 200.464655 -362.780298 849.901242 1924.841589
## [51] 12.152178 -638.879456 -941.614458 -249.751141 -544.259430
## [56] 613.095112 2144.982967 56.492234 -673.605034 -714.929799
## [61] 734.409142 -1017.947881 709.169097 926.134623 314.213722
## [66] -301.442700 -902.263971 -757.315173 -218.000102 753.252845
## [71] 658.741366 979.938784 -116.744733 -1140.500929 -1044.946079
## [76] -382.699557 -39.748928 279.519958 -112.654712 39.776547
## [81] 9.054967 -108.136916 -337.883654 -13.059014 766.977021
## [86] -297.850638 -1214.492617 -399.578901 -370.586129 -372.329514
## [91] 271.647958 775.077981 267.453636 -380.971438 -19.262260
## [96] -971.274860 46.638362 504.705617 1190.944510 238.729090
## [101] -1.571766 -971.795012 87.941385 -616.900429 644.123440
## [106] 1149.837957 387.031717 115.296221 -692.075346 -491.880934
## [111] -37.679522 541.707264 1448.094968 525.848622 -136.212910
## [116] 6708.217995 -1864.592652 -1484.170274 -236.420281 450.866777
## [121] -694.855397 692.691074 -206.709326 -556.217313
##
## $avar
## [1] 1432462
##
## $aic
## [1] 14.28781
##
## $aicc
## [1] 15.31404
##
## $bic
## [1] 14.44702Difference the data based on surfaced (1-B) Factor
Once the data has been differed we something that looks much closer to a stationary data set. However, we have also surfaced what appears to be a small seasonality component. We see the ACF have higher spikes surface at 7 and 14, which would lead us to believe there is a 7 day seasonal component.
us.diff = artrans.wge(us$hospitalizedCurrently, phi.tr = 1)
Seasonailty Transformation
Above we have surfaced what appears to be a 7 day seasonality trend. We will now transform the data for the s=7.
us.diff.seas = artrans.wge(us.diff,phi.tr = c(0,0,0,0,0,0,1))
Diagnose Model w/ aic.wge
When we diagnose the the best models to use for our stationary data set we see the AIC select a ARMA(5,1) model while the BIC selects a AR(2). The AR(2) model is consistent with our pseudo-cyclic data as well as the dampening cyclical sample autocorrelations that are produced by the transformed data. The ARMA(5,1) could also produce these same traits. We will move forward and compare these two models.
aic5.wge(us.diff.seas)## ---------WORKING... PLEASE WAIT...
##
##
## Five Smallest Values of aic## p q aic
## 17 5 1 14.58983
## 12 3 2 14.61706
## 14 4 1 14.63818
## 10 3 0 14.64214
## 13 4 0 14.64639aic5.wge(us.diff.seas,type = "bic")## ---------WORKING... PLEASE WAIT...
##
##
## Five Smallest Values of bic## p q bic
## 7 2 0 14.73106
## 10 3 0 14.73709
## 6 1 2 14.74186
## 8 2 1 14.75288
## 17 5 1 14.75600Diagnose white noise
Both of the Junge Box test show us that we reject the H null with pvalues that are < 0.05 alpha significance level.
ljung.wge(us.diff.seas)$pval## Obs 0.2551562 0.3832289 0.2777059 0.1275141 0.09296219 0.0898478 -0.2932202 0.0600709 -0.09689984 -0.0006399051 0.01526244 -0.02103579 0.01976312 -0.01353223 -0.05456826 -0.02766127 -0.09564359 -0.1088496 -0.08276253 -0.1151649 -0.1019156 -0.07946092 -0.06270657 -0.08635239## [1] 3.551215e-05ljung.wge(us.diff.seas, K=48)$pval## Obs 0.2551562 0.3832289 0.2777059 0.1275141 0.09296219 0.0898478 -0.2932202 0.0600709 -0.09689984 -0.0006399051 0.01526244 -0.02103579 0.01976312 -0.01353223 -0.05456826 -0.02766127 -0.09564359 -0.1088496 -0.08276253 -0.1151649 -0.1019156 -0.07946092 -0.06270657 -0.08635239 0.007035863 -0.04274568 -0.04721326 -0.0386816 -0.07346947 -0.05386179 0.01834432 -0.0629751 -0.02883663 -0.0004270837 0.00337915 0.01553369 -0.02742407 -0.05095818 -0.01418516 -0.01607667 -0.02314061 -0.01357636 -0.01505951 0.04436695 0.01818611 0.01944229 0.03469226 0.0006925423## [1] 0.04006747Estiamte Phis and Thetas
AIC Phi and Theta Estimates
est.us.diff.seasAIC = est.arma.wge(us.diff.seas, p = 5, q=1)##
## Coefficients of Original polynomial:
## -0.6073 0.5495 0.5896 0.0396 -0.3023
##
## Factor Roots Abs Recip System Freq
## 1+0.9499B -1.0528 0.9499 0.5000
## 1+1.0086B+0.6463B^2 -0.7802+-0.9687i 0.8039 0.3579
## 1-1.3512B+0.4923B^2 1.3722+-0.3850i 0.7017 0.0435
##
## mean(us$hospitalizedCurrently)## [1] 37955.28BIC Phi Estiamtes
est.us.diff.seasBIC = est.arma.wge(us.diff.seas, p = 2)##
## Coefficients of Original polynomial:
## 0.1529 0.4183
##
## Factor Roots Abs Recip System Freq
## 1-0.7277B 1.3741 0.7277 0.0000
## 1+0.5748B -1.7396 0.5748 0.5000
##
## mean(us$hospitalizedCurrently)## [1] 37955.28Forecasts
ARMA(5,1)
ARMA(5,1) Short Term
shortARMA <- fore.aruma.wge(us$hospitalizedCurrently, phi = est.us.diff.seasAIC$phi, theta = est.us.diff.seasAIC$theta, d= 1, s = 7, n.ahead = 7, lastn = FALSE, limits = FALSE)
- ASE
ASEshortARMA1 = mean((us$hospitalizedCurrently[(124-7+1):124]-shortARMA$f)^2)
ASEshortARMA1 ## [1] 4680969ASEshortARMA2 = mean((shortARMA$f-us$hospitalizedCurrently[(length(us$hospitalizedCurrently)-6):length(us$hospitalizedCurrently)])^2)
ASEshortARMA2## [1] 4680969- Windowed ASE
ARMA(5,1) Long Term
longARMA <- fore.aruma.wge(us$hospitalizedCurrently, phi = est.us.diff.seasAIC$phi, theta = est.us.diff.seasAIC$theta, d= 1, s = 7, n.ahead = 90, lastn = FALSE, limits = FALSE)
- ASE
ASElongARMA1 = mean((us$hospitalizedCurrently[(124-90+1):124]-shortARMA$f)^2)## Warning in us$hospitalizedCurrently[(124 - 90 + 1):124] - shortARMA$f:
## longer object length is not a multiple of shorter object lengthASElongARMA1 ## [1] 273191644ASElongARMA2 = mean((shortARMA$f-us$hospitalizedCurrently[(length(us$hospitalizedCurrently)-89):length(us$hospitalizedCurrently)])^2)## Warning in shortARMA$f -
## us$hospitalizedCurrently[(length(us$hospitalizedCurrently) - : longer
## object length is not a multiple of shorter object lengthASElongARMA2## [1] 273191644- Windowed ASE
phis = est.us.diff.seasAIC$phi
thetas = est.us.diff.seasAIC$theta
trainingSize = 25
horizon = 12
ASEHolder = numeric()
invisible(for( i in 1:(124-(trainingSize + horizon) + 1))
{
forecasts = fore.aruma.wge(us$hospitalizedCurrently[i:(i+(trainingSize-1))],phi = phis, theta = thetas, s = 7, d = 1,n.ahead = horizon)
ASE = mean((us$hospitalizedCurrently[(trainingSize+i):(trainingSize+ i + (horizon) - 1)] - shortARMA$f)^2)
ASEHolder[i] = ASE
})## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
## Warning in us$hospitalizedCurrently[(trainingSize + i):(trainingSize + i
## + : longer object length is not a multiple of shorter object length
invisible(ASEHolder)
hist(ASEHolder)
WindowedASE = mean(ASEHolder)
summary(ASEHolder)## Min. 1st Qu. Median Mean 3rd Qu. Max.
## 4887449 41116322 233726743 277361622 496865940 682241474WindowedASE## [1] 277361622i = 45
fs = fore.aruma.wge(us$hospitalizedCurrently[i:(i+(trainingSize+horizon)-1)],phi = phis, theta = thetas, s = 7, d = 1,n.ahead = 7, lastn = TRUE)
ASE = mean((us$hospitalizedCurrently[(i+trainingSize):(i+(trainingSize+horizon)-1)] - fs$f )^2)## Warning in us$hospitalizedCurrently[(i + trainingSize):(i + (trainingSize
## + : longer object length is not a multiple of shorter object lengthASE## [1] 4781164AR(2)
AR(2) Short Term
shortAR <- fore.aruma.wge(us$hospitalizedCurrently, phi = est.us.diff.seasBIC$phi, d = 1, s = 7, n.ahead = 7, lastn = FALSE, limits = FALSE)
AR(2) Long Term
longAR <- fore.aruma.wge(us$hospitalizedCurrently, phi = est.us.diff.seasBIC$phi, d = 1, s = 7, n.ahead = 90, lastn = FALSE, limits = FALSE)